CAHIER DE RECHERCHE #1305E WORKING PAPER #1305E Département de science économique Department of Economics Faculté des sciences sociales Faculty of Social Sciences Université d’Ottawa University of Ottawa

Do Men and Women Respond Differently to Competition? Evidence from a Major Education Reform*

November 2013

* I would like to thank Michael Baker, Branko Boskovic, Pierre Brochu, Victor Couture, Fernanda Estevan, Nicole Fortin, Caroline Hoxby, Josh Lewis, Rob�McMillan, Hessel Oosterbeek, Phil Oreopoulos, Uros Petronijevic, Joseph Price, Richard Romano, Aggey Semenov, Aloysius Siow, and seminar and conference participants at Carleton University, �l'Université de Sherbrooke, the University of Toronto, Wilfrid Laurier University, the November 2009 NBER Education Program Meeting, and the 2010 EALE/SOLE Meeting for many helpful comments. I am grateful to George Altmeyer, Khuong�Doan, Susan Pfeiffer, Pekka Sinervo, and the Faculty of Arts and Science at�the University of Toronto for making this project possible. All remaining�errors are mine. Disclaimer: The views, opinions, findings, and conclusions expressed in this�paper are strictly those of the author. † Department of Economics, University of Ottawa, 120 University Private (9056), Ottawa, Ontario, Canada, K1N 6N5; Email: lmorin@uottawa.ca.

Louis-Philippe Morin†

Abstract This paper provides new evidence of gender differences in response to increased competition, focusing on important life tasks performed in a regular social environment. The analysis takes advantage of a major education reform in Ontario that exogenously increased competition for university grades. Comparing students pre- and post-reform using rich administrative data, I find that male average grades and the proportion of male students graduating `on time' increased relative to females. Further, the evidence indicates that these changes were due to increased relative effort rather than self-selection. The findings have implications for the delivery of education and incentive provision more generally. Key words: competition, gender differences, higher education, performance, selection. JEL Classification: J16, I21. Résumé Ce document fournit de nouveaux signes de différences entre les sexes en rapport à leur réponse à une augmentation du niveau de compétition en se concentrant sur des tâches importantes réalisées dans un environnement social commun. L'analyse prend avantage d'une réforme majeure du système d’éducation secondaire en Ontario qui augmenta le niveau de compétition de manière exogène pour les notes universitaires. En Comparant les étudiants pré- et post-réforme à l'aide de riches données administratives, je trouve que les notes moyennes des hommes et la proportion d'élèves de sexe masculin diplômant ‘à temps’ s’accrurent par rapport aux femmes. De plus, les résultats suggèrent que ces changements sont dus à l'augmentation de l'effort relatif plutôt que l'auto-sélection. Les résultats ont des implications pour la prestation des services d'éducation et des mesures incitatives de manière plus générale. Mots clés : compétition, différences de genre, éducation postsecondaire, performance, sélection. Classification JEL: J16, I21.

1 Introduction

Experimental evidence from several recent studies, notably by Gneezy, Niederle, and Rustichini

(2003) and Gneezy and Rustichini (2004), indicates that males perform better than females in the

face of increased competition when carrying out specific laboratory tasks.1 These findings are highly

suggestive. They point to possible underlying differences in the cost of effort by gender, with effort

expenditure becoming less costly for men relative to women in more competitive environments. To

the extent that these differences carry over to important long-term tasks, they have the potential

to explain – at least in part – several striking features of the US labor market, including the

disproportionate presence of males in highly competitive jobs2 and gender inequalities in pay.

It is natural to view differences in labor market outcomes as the result of long-run exposure

to competitive environments in which individuals perform regular work-related tasks and are then

evaluated according to a competitive selection process or tournament. Ideally, to learn about

possible differential responses by gender to increased competition, one would like to mimic the

essential features of such a setting. This would include individuals performing day-to-day tasks

over an extended period – tasks that they are highly incentivized to care about – and drawing a

contrast between performance in low- versus high-competition environments while controlling for

all other relevant factors.

The pioneering experimental studies referred to above are able to vary competition exogenously

and cleanly control for potentially confounding factors. Yet the tasks these papers have focused on

– solving computer mazes and sprinting over short distances, for instance – are somewhat atypical.

To lend credence to the notion that underlying gender differences in response to greater competition

do indeed extend beyond the laboratory to regular activities in day-to-day life, this study analyzes

the impact of an exogenous change in competition on gender performance differences in a regular

social environment – the university classroom – focusing on life tasks that individuals have strong

incentives to care about. In this instance, the tasks involve trying to master the material covered

in university courses – somewhat analogous to skill accumulation in the workplace – with rewards

(in the form of grades) being based on relative performance over the course of the academic year.

More specifically, the analysis makes use of data from a major education reform in Ontario’s

secondary school system that shortened high school by one year, from five years to four. As a

consequence of this reform, which abolished the final year of high school (or Grade 13), two cohorts

graduated from high school in June 2003, creating a so-called ‘double cohort’ of students and

drastically increasing competition for university places that year. Importantly, given that capacity

did not increase anything close to proportionately, this in turn increased the quality of students

who ended up being admitted to university. For universities that grade on a fixed bell curve, like

1Gneezy et al. (2003) find that the relative and absolute performance of males increases as competition intensifies:males improve their performance while females do not.

2A variety of possible explanations for female under-representation in competitive jobs appear in the literature,including career-family trade-offs (Bertrand, Goldin, and Katz 2010), discrimination (Wolfers 2006), tastes for com-petition (Niederle and Vesterlund 2007), as well as differential performance in competitive environments (Gneezy etal. 2003).

1

the one studied here,3 the reform made it harder to receive higher grades. That is, each student

was now competing with higher quality (and more homogeneous) students for the same fixed grade.

In such circumstances, one would expect student effort to play a larger role in the determination of

university grades. The incentives to exert higher effort would increase alike for males and females,

but if males are more positively (or less negatively) affected by an increase in competition,4 then

such cross-gender differences could result in a differential shift in effort, manifesting itself as a

relative change in performance when comparing male and female outcomes.

It is worth noting that the word ‘competition’ in the context of classroom performance does

not have the same meaning as in the traditional experimental economics literature (e.g., Gneezy et

al. 2003). In this literature, researchers introduce competition by moving from a piece-rate payoff

scheme, where rewards are independent of the performance of others, to a payoff scheme where

the relative performance of other subjects matter (a ‘tournament’ pay scheme). In this paper,

student performance depends on the performance of her peers, even in the ‘non-competitive’ (pre-

reform) environment. Therefore, I study the impact of an increase in the level of competition.5

One could argue that the change in competition level observed here is closer to what we observe in

the workplace.

The first empirical goal of this paper is to see whether a differential performance shift occurred,

based on the increase in the level of competition in university classrooms due to the Ontario double

cohort.6 With that goal in mind, I examine the impact of increased competition on the gender

performance gap using data from the University of Toronto. In this case, the University of Toronto

provides a valuable context to shed new light on the gender effects of increased competition for

several reasons. First, with more than 55,000 undergraduate students, it is one of the largest

universities in North America and so affords very large samples. Second, I have access to rich ad-

ministrative data that allow me to observe virtually error-free performance measures for students

who attended university in a normal environment (before the double cohort) versus a more com-

petitive environment (entering university in September 2003), along with a set of useful controls.

Third, the grading scheme guidelines at the University of Toronto clearly indicate a ‘bell curve’-like

marks distribution throughout this time period, unlike other Ontario universities.

The data make it possible to estimate a set of regressions showing whether the relative univer-

sity performance of male students compared to females – i.e. the university gender grade differential

– improved in moving from a normal environment to a more competitive one, controlling for stu-

dent ability. Using this approach, I find that male students gained about 1 percentage point (or

11 percent of a standard deviation) over female students during their first year in university in

3I present the actual marking guidelines suggested to professors in Section 4, and show evidence of bell-curvemarking in Sections 4 and 6.

4For instance, men might enjoy being in a competitive environment more than females (or dislike it less).5In fact, the change in the level of competition observed in this paper makes it also close to some of the experimental

work done on the effects of affirmative action on effort (by changing the likelihood to win the tournament for someindividuals). See, for example, Calsamiglia, Franke, and Rey-Biel (2013).

6I focus on differential effort by gender while in university, though the empirics below address the possibility thatthere may have been effects in high school also.

2

response to the increased competition. While modest in size, the effect persists, remaining around

1 percentage point throughout students’ four years of university. The increased competition not

only affected student grades, but also influenced credit accumulation (especially for ‘below-average’

students) and on-time graduation rates, both suggesting that males became relatively more effective

as competition increased.

The second empirical goal of the paper is to shed light on the reasons for this differential

change in performance. In the observational setting of the double cohort, the performance change

might be attributable to differential changes in effort by gender – the hypothesized channel – but

also to differential selection and other changes by gender. Though student effort is not directly

observable, my approach makes use of the richness of the administrative data to address the most

likely potential self-selection issues and alternative channels. To the extent that selection and other

confounding factors do not appear to be significant, this points to differential changes in effort by

gender as the primary source of the measured performance differences.

On the selection front, the main concern is that competitive environments attract competitive

individuals and repel non-competitive individuals. Thus one might expect males (and especially

competitive males) to differentially select into the double cohort relative to females. Looking at

information on all applicants, regardless of whether they actually enrolled or not, the evidence

indicates that the double cohort did not have differential selection effects by gender. Specifically,

the proportion of females among applicants and enrolled students did not change significantly,

comparing the pre-reform period with the double cohort; nor did female representation within the

ability distribution (by high-school average quartile); and the proportion of female ‘fast-trackers’

– students from the Grade 13 program who graduated early and applied to university in 2002 –

did not change significantly either. I also investigate whether the increased competition affected

dropout and program-selection decisions differently by gender: the evidence does not show any

gender differences in these decisions. Overall, self-selection bias in this context does not appear to

be a cause for concern.

Ideally, one would randomly assign the competition treatment to some students and the con-

trol to others. But in the current observational setting, the students in the ‘high competition’

environment are clearly of higher ability than those attending university on the pre-reform period,

on average. Therefore, one necessary assumption for identifying the impact of competition on the

gender performance gap is that observable controls for ability are adequate.

One violation of this assumption serves as a potential threat to identification. Since competition

might have been tougher, not only in university classrooms but in high school also, the mapping

of student ability into high school grades could have changed in the following confounding way.

Suppose high school grades in the double cohort overestimated female student ability (relative

to males), then this could result in one overestimating male student performance in university

relative to females and falsely attributing this increase in performance to heightened university

competition. This scenario would require that females were more stimulated by competition than

males in both high school and university, but this differential would need to be smaller in university.

3

This seems unlikely given my findings relating to university performance: 1) the unconditional and

conditional university grades both suggest that the relative performance of males increased following

the double cohort, and 2) the female representation does not seem to have changed within the ability

distribution of applicants as competition increased.

Nevertheless, I address this possibility using information on out-of-province students and stu-

dents who attended a university prior to the University of Toronto, on the basis that the mapping

of ability into grades is not likely to have changed for these students. Estimating regressions using

only these students gives results that are very similar to the ones obtained using Ontario secondary

school students. Also, quantile regressions do not suggest that the differential impact of competi-

tion on performance by gender is driven by a specific type of student – whether low or high ability.

The evidence points to differential changes in effort by gender over the entire ability distribution.

The rest of the paper is organized as follows: The next section describes existing research on

gender and competition, and then explains how the Ontario double cohort can shed new light on

this topic. Section 3 sets out a model examining the potential impact of increased competition

in university, analyzing the implications for effort choice. Section 4 presents the data, and also

evidence of increased competition at the University of Toronto. The estimation strategy is described

in Section 5 and I present the main results in Section 6. Section 7 consists of a series of robustness

checks, in particular shedding light on whether the results are driven by self-selection. Section 8

then investigates whether increased competition also affected performance beyond students’ first

year in university, and Section 9 concludes, drawing out implications of the analysis.

2 Background

2.1 Prior Literature

This sub-section discusses the well-known research in experimental economics that first examined

how males and females respond to increased competition and also the small number of papers that

have looked at this issue in an observational setting.7

The experimental economics literature on competition and gender performance differences has

been motivated primarily by the findings in Bertrand and Hallock (2001). Those authors noted

that women only represent 2.5% of the 1992-97 ExecuComp dataset, consisting of the top five

executives in each firm of the S&P 500, S&P Midcap 400, and S&P Smallcap 600.8 Gneezy et

al. (2003) and Gneezy and Rustichini (2004) proposed and experimentally tested an explanation –

aside from discrimination or occupational self-selection – as to why we might observe large gender

differences in highly ranked (and highly competitive) labor market positions. Specifically, Gneezy

et al. (2003) conducted a laboratory experiment in which participants (university students) had

to solve as many computer mazes as possible in a given amount of time. While men and women

7For a more complete review of the literature on the topic, see Croson and Gneezy (2009), and Niederle andVesterlund (2010).

8Wolfers (2006) suggests that the female CEO representation is not improving as only 2.5 percent of new CEOappointments between 2000 and 2004 were females.

4

performed equally in the non-competitive environment, when placed in a more competitive environ-

ment, men significantly improved their performance while women did not. The authors concluded

that “women may be less effective than men in competitive environments.” Gneezy and Rustichini

(2004) presented evidence that this gender difference might hold at a young age as well, based on

a field experiment in which children had to sprint over a certain distance in different competition

settings. There also, boys’ performance was enhanced by direct competition while girls’ was not.

My paper investigates whether the findings in these pioneering studies also emerge in long-term

tasks involving a regular social environment. There is a clear link between my paper and Gneezy

et al. (2003): both studies compare performance across individuals and in both cases, one group

receives the (increased) competition treatment while the other does not. The main differences lie in

the contrasting nature of the tasks studied (solving computer mazes versus performing in university

courses) and the random assignment, which is only possible in the experimental setting. Note that

the nature of the task studied here – long-term and mattering for future life outcomes – is key

in gauging the potential of competitive gender differences to explain features of the labor market;

Section 7 of my paper tackles the selection issue.

Few papers have studied the effects of an ‘exogenous’ change in competition on performance in

observational (non-experimental) environments. Price (2008) looked at the effect of the introduction

of the Graduate Education Initiative (GEI), which increased competition within Ph.D. programs, on

the time to candidacy for students attending elite U.S. universities. The GEI sponsored fellowships

intended to reward“students who made the quickest progress toward completing their degree”(Price

2008). While males decreased their time to candidacy by ten percent, women were not affected by

the GEI. My paper analyzes a more common type of activity that a large fraction of the population

will have to deal with at some point in their life. In the course of doing so, it takes a close look at

the potential self-selection impacts of increased competition.

Two recent studies have looked at potential gender differences in performance on university

admission tests. Jurajda and Munich (2011) looked at whether females become relatively less likely

to be admitted in a university program as it becomes more competitive (as the admission rate of the

program decreases). Based on an entire cohort of Czech secondary-school graduates, each applying

to about three university programs, they find that female applicants are significantly less likely to

be admitted to most selective university programs relative to males with similar ability.

In the same vein, Ors, Palomino, and Peyrache (2013) studied gender difference in performance

in the highly competitive entry exam to the Master of Science in Management program at one of

France’s top business schools (HEC Paris). They found that males outperformed females in the

entry exam, while admitted female students outperformed their male counterparts during their

first year at HEC – a less competitive environment, according to the authors. They also found

that female HEC applicants outperformed male applicants in the baccalaureat exam, assumed to

be a less competitive pre-application exam.9 Note that the three types of exam studied by Ors et

9Niederle and Vesterlund (2010) suggest using caution when comparing the performance distribution of admittedstudents to the performance distribution of applicants as the former is a (highly) truncated subsample of the latter.

5

al. (2013) not only differed in their competition level, but also differed in their format (e.g. oral

versus written exams) and the skills (e.g. general versus management-specific knowledge) that they

tested. As with Price (2008), Ors et al. (2013) do not focus on the potential impact of competition

on gender differentials in self-selection.

My paper is also related to Lavy (2013) in that both studies look at a regular competitive

environment. Lavy (2013) examines a tournament-like pay scheme rewarding Israeli teachers who

performed better than their peers (based on the difference between the predicted and actual perfor-

mances of their students). Contrary to the studies cited above, Lavy (2013) does not find evidence

of gender differences in performance in this competitive workplace environment.

2.2 The Ontario Double Cohort

A key challenge in estimating the impact of competition on performance in a natural environment

is to find an exogenous source variation in the competition level faced by individuals. The abolition

of Grade 13 offers such a source.

As part of a major reform to its secondary school system, the government of Ontario announced

the abolition of Grade 13 in 1997. Prior to this reform, Ontario students entered college or university

after completing Grade 13, which contrasted with the other secondary school programs in Canada.

Following the reform, students were now expected to complete secondary school in four years (after

Grade 12) instead of five. The first cohort of the new program (henceforth referred to as the ‘G12’

program) began secondary school (Grade 9) in September 1999. Since students completed the new

program faster than its predecessor (the ‘G13’ program), the first cohort of the G12 program and

the last cohort of the abolished program were expected to graduate and apply to post-secondary

institutions in spring 2003, giving rise to the Ontario ‘double cohort.’

Figure 1: Number of Ontario University Applicants (in thousands)

Figure 1 shows the effect of the double cohort on the number of post-secondary institution

6

applicants. There was a significant spike in the number of applicants in 2003, increasing from

about 60,000 to more than 100,000 between 2001 and 2003. Since Ontario universities did not

expand capacity in proportion, this large increase in the number of applicants made university

access more difficult in 2003. We can see the impact of the double cohort on the selectivity of

universities by looking at the application numbers for the University of Toronto. The relevant

numbers for 2001 and 2003 are presented in Table 1.10

The increase in the number of applicants between 2001 and 2003 was 61.3 percent, which is

significantly greater than the increase in enrollment (25 percent). This led the enrollments-to-

applicants ratio to drop from 71 to 55 percent, indicating that university admissions became much

more competitive than in previous years.

Table 1: University Applicants and Enrollment

Applicants Enrollment Enr./App. App. Increase Enr. Increase

2001 10,349 7,300 0.71 - -2003 16,697 9,124 0.55 61.3 % 25.0 %

Source.–University of Toronto Admissions and Awards.

By increasing competition for university admissions, the double cohort also affected the quality

of students enrolled in university in 2003. It is natural to expect students admitted to a university

during the double-cohort year to be better than students admitted to the same institution a few

years before. The level of competition in university should also have been greater since each student

would be facing better (and more homogeneous) classmates in terms of high school averages. This

is especially true if relative performance is an important component of university grades, as the

increased homogeneity in student ability and a fixed ‘bell curve’ can increase the role of effort in

determining university grades (as explained in the next section).

It is worth noting that there was a significant increase in the number of applicants in 2002

relative to 2001, looking ahead to some of the selection issues that will be addressed in Section

7. Although this increase is smaller than in 2003, it does suggest that some G13 students escaped

the double cohort by ‘fast-tracking’ secondary school.11 If more females tried to avoid the double

cohort by fast-tracking, the populations of male and female students who entered university in

2003 may not be comparable. The evidence presented below indicates that this is not an issue.12

Also, comparison of the female representation by high-school average quartile between 2001 and

2003 indicates that the female representation did not change significantly within the student ability

distribution (see Table 2 in Section 4.1).

10This is the number of students who put the University of Toronto as their first choice institution when applyingthrough the Ontario Universities’ Application Centre (OUAC). The number of students who put the Universityof Toronto as their first, second, or third choice was around 64,000 for 2003-2004. Source: University of TorontoAdmissions and Awards.

11It was possible for G13 students to fast-track secondary school, but only a small number of them would do so.Between 1996 and 2001, the proportion of Ontario university students who had graduated from high school after fouryears fluctuated between 7.7 and 8.5 percent (King et al. 2002).

12I investigate this possibility in Section 7.2, but do not find any significant change in the proportion of femalefast-trackers in 2002.

7

3 Increased Competition, Bell-Curve Marking, and Effort

In this section, I first examine the impact of increased competition following the double cohort

on the link between high school grades and university grades. In particular, I present predictions

regarding the expected signs of the parameter estimates from regressing university grades on high

school grades if a university grades its students based on a bell curve. This will allow me to verify

later on that competition really did increase in university classrooms following the double cohort. I

then present a simple model that illustrates a possible channel through which performance gender

differences can emerge as competition increases: differential changes in effort incentives.

3.1 Increased Competition and Grades

This subsection makes explicit the way that increased competition can affect the link between

ability (measured by high school grades) and university performance.

Suppose that, for every student i enrolled in university in year t, we observe a university grade,

Ui,t, and a high school grade, Hi,t. Assume that the university grades on a fixed bell curve such

that, every year, university grades follow a normal distribution with the same mean µU and variance

σ2U . Further, assume that Hi,t also follows a normal distribution, but with mean µH,t and variance

σ2H,t are allowed to vary over time.13 We can link the two distributions using:

µU = at + btµH,t (1)

and

σ2U = b2tσ2H,t (2)

where bt is expected to be positive.

Figure 2 illustrates the link between high school and university grades. The top panel of Figure

2 presents the distribution of high school grades of students admitted to university while the bottom

panel presents the distribution of university grades.

Assume that competition for university admission increases between t and t′. As competition

increases, the distribution of high school grades admitted to university will shift to the right – the

average will increase from µH,t to µH,t′ – and, in turn, the variance, σ2H,t, will decrease. These

changes in mean and variance are simply due to the limited admission capacity of the university.

This phenomenon is illustrated in the top panel of Figure 2.

Since the university keeps the same performance distribution from year to year (i.e. µU and

σ2U remain unchanged), the increased competition will affect the link between high school grades

and university grades. In the top panel of Figure 2, we can see that σ2H,t decreases as competition

increases. Therefore, bt′ will be larger than bt (from a less competitive year) to guarantee that

equation (2) still holds. Also, since both µH,t and bt increase, at will decrease to ensure that

equation (1) is satisfied.

13Figure 4, below, suggests that a normal distribution is a reasonable approximation to the actual grade distribution.

8

Figure 2: Increased Competition, Bell-Curve Marking Scheme and Grades

9

The framework presented above makes two predictions regarding the parameter estimates from

estimating an equation of the following form:

Ui,t = α+ γHi + πDCt + ρ(DCt ×Hi) + ωi,t. (3)

where Ui,t is student i’s university grade, Hi is student i’s high school grade and DCt is a dummy

variable equal to 1 if student i is observed during the more competitive year. Equation (3) can

be seen as the base regression equation used in this paper. Here, π and ρ will capture changes

in the constant and slope parameters in equation (1) (i.e. π = at′ − at and ρ = bt′ − bt from the

earlier discussion) following the increase in competition. If the university grades on a bell curve,

we should first expect the slope coefficient to be greater (ρ > 0) and second, the intercept to be

smaller (π < 0) in more competitive years. Note that these predictions are easily testable with the

available data. The regression results in Section 6 suggest that ρ > 0 and π < 0.

3.2 Increased Competition and Effort in University

The previous model made explicit the link between competition, grades, and bell-curve marking. I

now present a simple model to analyze the potential impact of increased competition and bell-curve

marking on the effort incentive in university classrooms.

Imagine students with ability a will exert effort e when studying to acquire knowledge, K(e, a).

Assume that K(e, a) is continuously differentiable, increasing and concave in e and a. The cost of

studying is given by a continuously differentiable function Cg(e, a, l) (in e and a), and increasing

and convex in e – these assumptions yield well-behaved marginal cost and marginal benefit of effort

schedules. The cost to studying also depends on the student gender g ∈ {f,m} and the level of

competition l in the classroom. Increases in the level of competition will decrease the marginal cost

of studying if students enjoy competition. Suppose that in the absence of competition (at l = 0),

males and females have the same cost functions:

Cf (e, a, 0) = Cm(e, a, 0) = C(e, a, 0)

Therefore, females and males are expected to exert the same level of effort and perform equally for

a given a – they have the same knowledge production and cost functions at l = 0.

Assume that males enjoy an increase in the level of competition more than females, in the sense

that the marginal cost of effort decreases more for males as the level of competition increases:14

∂C2f (e, a, l)

∂e∂l>∂C2

m(e, a, l)

∂e∂l

Now, the university grades its students according to the following scheme:

G(e, a, l) = ηl + λlK(e, a)

14The results are exactly the same if they dislike competition less than females.

10

where the university adjusts ηl and λl to satisfy its bell-curve marking scheme. In particular, the

university is expected to increase the benefit to effort by increasing λl (and to decrease ηl) in a

more competitive year.15 Student utility is simply defined by the difference between the university

grade and the cost of studying. Therefore, the student utility maximization problem is:

maxe

ηl + λlK(e, a)− Cg(e, a, l)

The first-order condition for this problem is

λl∂K(e∗g, a)

∂e−∂Cg(e

∗g, a, l)

∂e= 0 (4)

The question is whether male effort will increase more than for females when we move from a

non-competitive environment (l = 0) to a competitive environment (l > 0). Figure 3 illustrates

how female and male levels of effort will change following an increase in the level of competition.

The details relating to this comparative statics exercise are in Appendix B.

First, recall that in the absence of competition (at l = 0), females and males are assumed to

have the same knowledge production and cost functions. Therefore, in the absence of competition,

females and males will both choose an effort level equal to e∗(a, l = 0). An increase in competition

will affect both the marginal benefit (by increasing λl) and the marginal cost of exerting effort. The

increase in marginal benefit will be the same for females and males, but the change in marginal cost

will differ if males enjoy competition more than females. More specifically, males will experience

a more pronounced rightward shift of their marginal cost curve than females. Consequently, male

effort will shift from e∗(a, l = 0) to e∗m(a, l > 0) while female effort level will only shift from

e∗(a, l = 0) to e∗f (a, l > 0) (in Figure 3). Under these circumstances, an increase in competition is

expected to differentially affect the effort level of females and males.

4 Data

In order to look at the effect of the increased competition in university classrooms on academic

performance, I focus on students who enrolled at the University of Toronto – one of the largest

universities in North America. I use an administrative data set provided by the University of

Toronto Faculty of Arts and Science that is composed of first year students who started in Arts and

Science in September 2001 or September 2003.16 In 2010, close to 22,000 undergraduate full-time

students were attending University of Toronto’s Faculty of Arts and Science, making it the largest

faculty of the University.

15In Appendices B.1 and B.2, I present a model that shows the impact of increased competition on the effortincentives set by a university that grades on a bell curve. I show that under mild conditions (depending on the‘complementarity’ between effort and ability), the university will increase λl as competition for university admissionincreases.

16For related studies using college administrative data, see Sacerdote (2001) using Dartmouth College data, Stine-brickner and Stinebrickner (2006) using Berea College data, Angrist, Lang, and Oreopoulos (2009), Hoffmann andOreopoulos (2009a, 2009b) and Lindo et al. (2010) using data from a large Canadian university.

11

Figure 3: Increased Competition and Effort Level

The Faculty of Arts and Science combines three features necessary for the analysis of competition

on grades. First, and most importantly, the institution analyzed must grade its students based (at

least implicitly) on a bell curve. Unlike a number of Ontario university faculties, the Faculty of

Arts and Science had specific guidelines for the marks distribution, clearly suggestive of a bell-curve

marking scheme.17 Second, the Faculty has large introductory classes – many of these classes are

compulsory (for a given program) and some of them have more than 1,000 students – making it

possible to get relatively precise estimates. Third, most study subjects offered by the Faculty were

not affected by the Ontario Secondary School reform.18 This is not the case with other faculties.

17Until 2009, the “Academic Handbook: Course Information for Instructors” that was available on the Universityof Toronto Faculty of Arts and Science website (http://www.artsci.utoronto.ca) we could read that, although notrequired, experience suggests that there will normally be between 5% and 25% of A’s, not over 75% of combined A’sand B’s, and not over 20% of combined E’s and F’s in large classes. Since 2009, the marks distribution guidelines areslightly broader.

18The compression of the Ontario secondary school curriculum affected the delivery of material for some subjectsand not others. For example, the Mathematics curriculum was affected, while the Biology curriculum was not (Morin

12

The data come from two sources of information that were linked using students’ identification

numbers: pre-university admission information and university academic histories. The university

academic history contains 1) the numerical grades for all Arts and Science courses that the student

completed, 2) the list of courses that the student dropped (along with the dates these courses

were dropped), and 3) a dummy variable, ‘on-time’ graduation, indicating whether the student had

graduated from university by July 1st of her fourth year (e.g., July 1st 2007 for 2003 students).

The main dependent variable consists of individual course grades, on a 100-point scale. I focus

on performance in larger classrooms (i.e., with at least 30 students) since bell-curve marking in

smaller classrooms is less likely and that this type of marking scheme is assumed to be a driving

factor behind my results. About 90 percent of first-year grades come from these larger sections.

As a robustness check, I present the results from smaller classrooms in Section 6.3. I also look at

students’ first-year (credit-weighted) averages (on a 100-point scale), their GPA, dropped courses,

credit accumulation, and ‘on-time’ graduation.19 Although I eventually look at student performance

from their first through fourth university years, I concentrate the analysis on first-year performance.

An obvious advantage of doing so is that it mitigates much of the potential impact of course

selection, as many of first-year courses are, as noted, compulsory given a specific program of study.

A nice feature of the data is that it contains pre-university admission information for students

who applied to the Faculty of Arts and Science, regardless of whether their application was accepted

or rejected. Hence, this information will be used not only to control for students’ backgrounds but

also to look for evidence of increased competition in university admissions. This information will

also be crucial to investigate whether females tried to avoid the increased competition (more than

males) by choosing ‘less competitive’ programs, or simply by not applying/enrolling to the university

in 2003, which is plausible if one thinks that females are more likely to “shy away from competition”

(Niederle and Vesterlund 2007).

For each applicant, I have the following information: a student identification number, the

applicant’s high school average, her/his year and month of birth, and her/his gender, the name

of the school attended by the applicant, the Faculty program applied to (Commerce, Computer

Science, Humanities and Social Sciences, or Life Science), and application status (enrolled, accepted,

canceled, or refused).20

I restrict the sample to Ontario high-school graduates born in 1984 and 1985 for the 2003

2013). See King et al. (2002, 2004, 2005) and Morin (2013) for more details. As explained below, all Mathematicscourses are excluded from the analysis.

19Students earn 0.5 credits for successfully completing a one-semester course and a 1.0 credit for successfullycompleting a two-semester course. As students take one- and two-semester courses, the student first year average isweighted by the credit units. I computed first-year averages for all students for which I observe at least two numericalgrades by the end of the first year. I consider that students who report grades under 30 percent have, in fact, droppedthe course. These course outcomes will be used, with the courses that were officially dropped, to see whether females(or males) were more likely to drop courses (or ‘stop competing’) in 2003. As discussed in Section 7.1, including thesegrades would actually make my results slightly stronger.

20Students interested in a specific study program offered by the University of Toronto Faculty of Arts and Sciencehave first to apply to one of the following general programs: Commerce, Computer Science, Humanities and SocialSciences, or Life Science. Enrolled status entails application acceptance (from the Faculty) and the student choosingto enroll.

13

student cohort, and in 1982 for the 2001 cohort in order to avoid having the results affected by

older students.21 Out-of-province students and students who already had some university experience

before applying to the Faculty will be used in Section 7.3 for robustness checks.22

The data contain an indicator of the secondary school curriculum (Grade 12 or Grade 13) the

student graduated from. The G12/G13 indicator is necessary for performing the analysis with

or without G12 students. There are pros and cons to including G12 students in the sample.

Focusing on G13 students (excluding G12 students from the sample) guarantees that, aside from

potential differences in academic ability, students from 2001 and 2003 should be quite similar in

terms of academic background (e.g. they come from the same secondary school program) and other

dimensions such as maturity – since students have the same age. But, if Grade 13 had a significant

impact on students’ university preparation and if gender composition differs across G12 and G13,

then not including G12 students could over- or underestimate the effect of the double cohort on

gender differences in performance. In addition, Morin (2013) presents evidence that G12 students

who entered university in 2003 were better-than-average students. If this is the case, and if the

gender composition differs across G12 and G13 students, then excluding G12 students could also

result in biased estimation of the competition effect, even if we assume no difference in university

preparation across curricula. For this reason, the estimations were all done with and without G12

students. Results show that including or excluding G12 students give very similar estimates.

Finally, the secondary-school Mathematics curriculum was clearly affected by the reform (Morin

2013). Since female and male students might have reacted differently to the change in Mathematics

curriculum, all Mathematics courses were excluded from the analysis.23 This should mitigate any

potential bias due to differences across G12 and G13 university preparation. In practice though,

including Mathematics performance in the university average does not affect my results.

4.1 Evidence of Increased Competition

The drop between 2001 and 2003 in the enrollment/application ratio presented in Table 1 already

suggests a significant impact of the double cohort on university admission. Table 2 presents descrip-

tive statistics used to look at the effect of increased competition on student university performance.

The key point coming out of Panel A is that the double cohort significantly increased competi-

tion for university admission and the quality (based on students’ high school average) of enrolled

students. The average high school grade increased by close to 2.6 percentage points between 2001

21The birthday cutoff date for primary-school enrollment is December 31st in Ontario. Hence, students from thefirst G12 cohort are supposed to be born in 1985, while students from the last cohort of the G13 program should beborn in 1984. As a robustness check, I also estimated the regression model including older students. The inclusion ofthese students does not affect the results.

22Pre-admission information from many out-of-province students is missing since they do not necessarily applythrough the same process as Ontario high-school graduates. Admission information for these out-of-province studentsis kept by the colleges to which they applied to, and not by the Faculty of Arts and Science.

23There is a large literature on the gender gap in Mathematics. Interested readers should consult Ellison andSwanson (2010), Fryer and Levitt (2010), and Niederle and Vesterlund (2010) for recent developments in the topic.

14

Table 2: Descriptive Statistics

2001 2003G13 G12 G13

A. Main Descrptive Statistics:HS Average 85.4 88.2 87.9

(4.86) (4.41) (4.43)Age 19.2 18.2 19.2

(0.28) (0.28) (0.28)Female (%) 61.1 62.4 61.3Observed in Year 2 (%) 90.0 91.7 92.4Observed in Year 3 (%) 77.3 84.5 82.1Observed in Year 4 (%) 71.9 78.1 75.3First Year University Average* 69.7 71.2 70.8

(9.30) (9.94) (9.42)Attempted Credits (First Year)** 4.01 4.10 4.13

(0.80) (0.70) (0.79)Earned Credits After 1 Year** 3.84 3.92 3.94

(0.96) (0.91) (0.98)Earned Credits After 4 Years** 13.1 14.9 14.5

(4.55) (4.77) (4.90)‘On-Time’ Graduation (%) 39.9 42.1 38.4

B. Females by HS Average Quartile (%):Bottom Quartile 56.0 56.5 55.3Second Quartile 60.4 64.2 60.1Third Quartile 62.3 66.4 64.2Top Quartile 65.8 62.7 65.7

Observations 2,463 1,702 1,835

Note.–* Excludes grades from smaller classes (i.e. with less than 30 students) and

Mathematics grades. ** Excludes Mathematics credits. The number of credits

earned is zero for year X (X=2, 3, or 4) if the student is not observed in year X.

Standard deviations are in parentheses.

and 2003. This difference is statistically significant and considerable – representing an increase of

55 percent of a standard deviation (relative to 2001).

The increased in student quality between 2001 and 2003 can be illustrated by comparing the

distributions of enrolled students’ high-school averages. The top panel of Figure 4 plots estimated

densities of high school averages for students enrolled at the Faculty of Arts and Science in 2001

and 2003. Clearly, students enrolled in 2003 have higher high school averages than students who

enrolled in 2001.

What further suggests that competition increased in university classroom is the use of bell-curve

grading in university. The university average was around 70 percent in 2001 and increased by about

1.4 percentage points (less than 15 percent of a standard deviation) in 2003. As can be seen from

the bottom panel of Figure 4, this increase is significantly less (in absolute or relative terms) than

the increase high school averages, suggesting that it became harder to get higher grades. Credit

15

Figure 4: High School Average Distributions of Enrolled Students

accumulation and ‘on-time’ graduation also suggest a modest performance increase between 2001

and 2003. In sum, evidence from Figure 4, and Tables 1 and 2 all suggest that competition in

classrooms increased significantly as a consequence of the double cohort.

As expected, G12 students are on average exactly one year younger than G13 students (see

Panel A of Table 2). The student population is composed of a majority of female, comprising more

than sixty percent of the population. Of note, the proportion of female did not change significantly

between 2001 and 2003. This is important evidence, especially if one is concerned that there could

be significant gender differences in the taste for competition.

Panel B of Table 2 presents the proportions of female students by high-school-average quartile

to further investigate whether there were significant changes in the female representation. Females

tend to be slightly less present in the bottom quartile. There was, however, no drastic change

in the female representation by quartile between 2001 and 2003. This is especially true if we

compare the 2001 and 2003 G13 students. This is important evidence as it suggests that the female

16

representation did not change significantly within the ‘ability’ distribution – something that could

signal some significant selection issues.

5 Estimation

The main estimation strategy used to gauge the effect of increased competition on gender perfor-

mance differences is captured by the following extension of equation (3):24

Ui,t = α+ γHi + δMalei + πDCt + ρ(DCt ×Hi) + β(DCt ×Malei) + XiΓ + ωi,t. (5)

Ui,t is a university performance measure (the student’s university average, the number of university

credits earned, or on-time graduation). The main outcome of interest is a student’s performance

in large first-year university course Ui,t,c (where c stands for a specific course). For this specific

outcome, equation (5) is augmented with course fixed effects, ψc. One of the main benefits of

looking at first year performance is that during this year, the choice of courses is not as important

as for later years, which can mitigate potential course selection issues. Furthermore, first-year

courses usually have very high enrollments, as mentioned above.

Hi is a measure of student ability (high school average), while Malei and DCt are a male

and a double-cohort-year dummy variables, respectively. Finally, Xi is a vector of other personal

characteristics. The coefficient of interest is β which represent the difference, across genders, in

the effect of the double cohort. The coefficients π and ρ will capture common effects (to males

and females) of the increased competition. Notice that the estimates of π and ρ are expected to

be negative and positive, respectively (as in equation (3)). δ allows one to test whether (ceteris

paribus) males perform better than females in university. Xi will consist of controls like program

fixed effects and age, which will be added to the equation in some specifications. Controlling for

age could be useful when including G12 students in the analysis.

6 Results

6.1 Competition and First Year Performance

Figure 5 shows the evolution of the university first year average distributions between 2001 and 2003

for males and females separately, already pointing to gender differences in response to the increased

competition following the double cohort. First, the top panel of Figure 5 shows that male and

female pre-double cohort (2001) performance distributions are similar. A Kolmogorov-Smirnov test

for equality of distributions suggests that the two distributions are identical. Things are different

in 2003: We see a clear shift to the right for both males and females (in the bottom panel),

suggesting that the unconditional student performance increased in 2003. More importantly, the

24Quantile regressions are also estimated in Section 6.2 to investigate the possibility of heterogeneous effects ofcompetition on the university performance distribution.

17

distributional shift for males is more pronounced – the male and female performance distributions

are now statistically different. Interestingly, when comparing the female and male 2003 performance

distributions, the male distribution looks, more or less, like a translation (to the right) of the female

distribution. Although Figure 5 only plots ‘unconditional’ performance distributions, the regression

results presented in Table 3 and quantile regression results presented in Section 6.2 will support

the idea that the difference in the shifts in performance distributions captures the effect of the

increased competition (as opposed to changes in student characteristics).

Figure 5: University Average Distribution

18

Table 3: Impact of the Double Cohort on the Gender Performance Gap (Individual Courses)

G13 Students Only G12 and G13 Students(1) (2) (3) (4) (5) (6)

HS Average 1.074*** 1.176*** 1.177*** 1.074*** 1.152*** 1.153***(0.041) (0.050) (0.050) (0.041) (0.049) (0.049)

Double Cohort -11.86** -15.51*** -15.38*** -18.05*** -20.92*** -20.94***(4.893) (4.439) (4.441) (4.570) (4.283) (4.285)

Male 0.908*** 0.843*** 0.862*** 0.908*** 0.782*** 0.790***(0.284) (0.235) (0.235) (0.284) (0.251) (0.252)

HS Average × DC 0.117** 0.152*** 0.150*** 0.187*** 0.215*** 0.214***(0.054) (0.050) (0.050) (0.051) (0.048) (0.048)

Male × DC 1.061*** 1.019*** 1.009*** 1.042*** 1.014*** 1.015***(0.362) (0.348) (0.345) (0.341) (0.342) (0.341)

Age -0.778*** -0.329**(0.232) (0.151)

Course Fixed Effects No Yes Yes No Yes YesObservations 18,152 18,152 18,152 25,501 25,501 25,501Students 4,298 4,298 4,298 6,000 6,000 6,000R-squared 0.225 0.245 0.245 0.238 0.249 0.249

Note.–The dependent variable in these sets of regressions is a first-year university course grade. Clustered stan-

dard errors (at the course level) are in parentheses. * significant at 10%; ** significant at 5%; *** significant at

1%.

Table 3 presents results from estimating the course-level version of equation (5) with a course

grade (on a 100-point scale) as the dependent variable for different sets of controls, and for different

subsamples. The results in Table 3 will shed light on 1) whether it became harder to get high

grades as a consequence of the double cohort (i.e. whether the university graded on a ‘bell curve’),

and 2) whether (on average) males’ performance significantly improved relative to females.

Columns (1) to (3) only include students who graduated from the G13 program while columns

(4) to (6) also include students who graduated from the G12 program. The effect of the increased

competition on the university grading policy slope and intercept coefficients (π and ρ in equation

(5)) are captured by ‘Double Cohort’ and ‘HS Average × DC’ respectively. ‘Male × DC’ gives an

estimate of the difference across genders in the effect of the increased competition (β).

Results in column (1) do not include any personal characteristics aside from students’ high

school average and gender. The estimates for the changes in the university grading policy slope

and intercept coefficients have expected signs (ρ > 0 and π < 0) supporting the idea of increased

competition in classrooms in 2003. These results suggest that university grades did not fully adjust

for the increased quality of students in their classrooms. This is to be expected if we think that

many universities recommend implicitly or explicitly a bell-curve marking scheme. Not surprisingly,

the effect of the double cohort on university grades is statistically significant. An ‘average’ 2003

female student – with an 88-percent high-school average – had a 1.56 percentage point (about 0.17

s.d.) disadvantage when compared to a similar student who entered university in 2001.25

2588 × 0.117 − 11.86 ≈ −1.56. The null hypothesis H0 : π + 88ρ = 0 is rejected at a 1 percent confidence level.

19

The estimated change in the gender performance gap due to the increased competition (1.06

percentage points) is statistically significant at the 1 percent level, but modest (0.114 s.d.), suggest-

ing that males coped better with the increased competition than females. These results are in line

with the findings of Gneezy et al. (2003) and Gneezy and Rustichini (2004). Note that, contrary to

Gneezy et al. (2003) and Gneezy and Rustichini (2004), I can only measure a relative (as opposed

to absolute) change in performance due to the increased competition, since the university seems to

be grading on a bell-curve (given the estimated coefficients for ρ and π).

The effect of the double cohort varies significantly across the student population. For example,

imagine two female students, one with a high school average one standard deviation (4.4 percentage

points) below and the other one standard deviation above the 2003 mean high school average (88

percent). The student below the mean would have had a 2.05 percentage point disadvantage from

being part of the double cohort. For the student above the mean, the disadvantage would be

significantly smaller (1.02 percentage points).

Allowing for course fixed effects and age control (columns (2) and (3)) does not alter the findings.

The coefficients on high-school average and ‘Male × DC’ are very stable across specifications.

Finally, the age effect is statistically significant but modest and negative: when comparing the

youngest and oldest students coming out of the G13 program, we expect the youngest students to

have a 0.78 percentage point advantage over the oldest.

Columns (4) to (6) replicate the estimates in columns (1) to (3) using the complete sample of

Ontario students, including both G13 and G12 students. The inclusion of G12 students does not

affect the estimated impact of increased competition on the gender difference in performance; it

remains around 1 percentage point.

One might think that the effect is modest enough not to have any impact on students’ GPA.

Using student GPA (on a four point scale) or a credit-weighted average (on a 100 point scale) as

dependent variable gives very similar to the ones presented in Table 3. The estimates for ‘Male

× DC’ when using students’ credit-weighted average fluctuate between 1.03 and 1.13 points and

between 0.08 and 0.10 GPA points when using students’ GPA (or between 0.10 and 0.11 s.d.).

These results are presented in Tables A1 and A2, respectively. In the end, all three measures of

university performance (i.e. course-level performance, GPA, credit-weighted average) suggest that

male students coped better with the increased competition than females.

6.2 Heterogeneity

The least-squares regressions capture the effect of increased competition on the average female-

male performance difference. Although informative, they may mask important heterogeneity in the

impact of competition. The least-squares estimates could, for example, be driven by a specific group

of students, such as male students in the upper tail of the performance distribution, who react more

to competition than the rest of the student population. In this case, the increased competition would

In order to convert the effect in terms of standard deviations, I use the 2001 university-average standard deviation(9.30) as found in Table 2. −1.56/9.3 = −0.168.

20

affect the shape of the performance distribution. In order to investigate this possibility, I estimated

equation 5 using a quantile regression methodology proposed by Firpo, Fortin, and Lemieux (2009)

and where the dependent variable is students’ first-year (credit-weighted) averages (the averages

plotted in Figure 5). This methodology allows one to estimate the impact of ‘Male × DC’ on

the quantiles of the unconditional university performance distribution, shedding light on a possible

increase in performance dispersion due to the increased competition.

Figure 6: Quantile Regression Estimates

Figure 6 plots the quantile regression ‘Male × DC’ estimates for the 5th to the 95th quantiles

and its 90 percent confidence interval band.26 The effect of competition on the gender performance

gap seems relatively stable over the performance distribution as the least-squares point estimate

is covered by the entire quantile regression band. What is clear from the quantile regression

results above is that estimated effects of the increased competition on the gender performance

gap found above are not overwhelmingly driven by effects at specific points (say top or bottom)

of the university performance distribution. They further suggest that the difference in the shift

in performance distributions found in Figure 5 is a reasonable illustration of the impact of the

increased competition on the gender performance gap.27

26The 90 percent confidence band is based on bootstrapped standard errors. The standard errors of each quantileare obtained from 500 replications.

27An alternative, albeit more restrictive, strategy to investigate the possibility of heterogeneous effects is to addinteraction terms (i.e. Male × HS × DC, with and without Male × HS) to equation (5). The parameter estimates ofthese interaction terms are always small and statistically insignificant at conventional confidence levels.

21

6.3 Smaller Sections

Evidence from Table 3 suggests that instructors graded on a bell curve in large classes – recall

that the sign of coefficient estimates for ‘Double Cohort’ and ‘HS Average × DC’ are in line with

bell-curve marking. I argue earlier that this bell-curve marking combined with the increased quality

of students gave rise to an increase in the level of classroom competition. However, we should not

expect the same kind of effects in smaller classes, as the suggested grading-scheme (see footnote

17) was intended for larger classes (e.g. with more than 20-30 students). Therefore, the increase

in competition for grades should be lower in smaller classes and we should expect the effect of the

double cohort on the gender performance gap to be minimal.

In order to investigate whether there was evidence of bell-curve marking in smaller classrooms,

and to see whether I find any evidence of a double-cohort effect on the gender performance gap, I re-

estimated equation (5), but using only grades from sections with less than 30 students.28 Table A3

does not suggest that instructors mark on a bell curve in these smaller classes: the coefficient

estimates for ‘Double Cohort’ and ‘HS Average × DC’ are small in magnitude (compared to the

ones found in Table 5) and have the opposite signs that we would expect if instructors were to

grade on a bell curve. Table A3 not only suggests that instructors do not grade on a bell curve, but

also that the increased student quality did not affect the gender performance gap in these smaller

classes: the coefficient estimates for ‘Male × DC’ are all small, fluctuating between −0.166 and

0.271, and statistically insignificant. The combination of these two findings support the idea that

bell-curve marking could be a crucial driving factor behind the change in gender performance gap

observed following the double cohort – when there is an increase in student quality.

7 Selection Issues

The results presented so far suggest that male students coped better with the increased competition

than females. These results do not take into account the possibility that students are more or less

free to drop out of courses/programs, to enroll, and to apply to university, or that competition might

have increased not only in universities, but in secondary schools as well. This section investigates

self-selection problems and looks at the potential consequences of increased competition at the

secondary-school level on the estimates presented so far. I start by considering the possibility

that males dropped out of courses disproportionately more than females as a consequence of the

double cohort, which would (probably) lead me to overestimate the gender difference in performance

in 2003. Next, I use the available admissions data to investigate any gender differences in the

enrollment or application decisions – the admissions data allow me to observe any student who

applied to the Faculty of Arts and Science (whether they were accepted or not). I also look at

28The class size cutoff was put at 30 students per section, instead of 20, to have a decent number of observationswhen running the regressions, while having a class size small enough not to expect bell-curve marking. 11.1 percentof first-year grades come from sections with less than 30 students, while only 4.7 percent come from sections withless than 20 students.

22

pre-university competition and its potential impact on the link between students’ ability and their

high-school average (the ability measure used in this paper).

7.1 Dropouts

If there are important gender differences when it comes to dropping a course, then the estimates

presented above may over- or under-estimate the full impact of the increased competition on uni-

versity performance. If, for example, the 2003 male students that were more adversely affected by

the increased competition dropped out of courses in a disproportionate way relative to their female

counterparts, then the findings presented in Section 6.1 could overestimate the gender performance

differential – the results could be due to selection. In order to investigate this issue, I looked at

individual courses, and constructed a dummy variable equal to 1 if a course was dropped, and 0

otherwise.29 I then estimated a linear probability model, using the same six specifications used to

estimate the effect of competition on grades, to test whether female and male dropout decisions

were affected differently by the increased competition.

Table 4: Impact of the Double Cohort on Dropped Courses

G13 Students Only G12 and G13 Students(1) (2) (3) (4) (5) (6)

HS Average -0.007*** -0.007*** -0.007*** -0.007*** -0.007*** -0.007***(0.001) (0.001) (0.001) (0.001) (0.001) (0.001)

Double Cohort 0.214** 0.222** 0.218** 0.086 0.090 0.089(0.100) (0.102) (0.101) (0.079) (0.077) (0.077)

Male 0.007 1.26e-4 -4.05e-4 0.007 4.37e-4 7.08e-05(0.008) (0.006) (0.006) (0.008) (0.006) (0.006)

HS Average × DC -0.002** -0.002** -0.002** -0.001 -0.001 -0.001(0.001) (0.001) (0.001) (0.001) (0.001) (0.001)

Male × DC -0.001 0.002 0.002 -0.006 -0.003 -0.004(0.008) (0.008) (0.008) (0.008) (0.008) (0.008)

Age 0.025*** 0.017***(0.006) (0.004)

Course Fixed Effects No Yes Yes No Yes YesObservations 19,793 19,793 19,793 27,640 27,640 27,640R-squared 0.021 0.019 0.020 0.019 0.016 0.017

Note.–The table reports the estimates of regressions of a dummy dependent variable equal to 1 if the course was

dropped, 0 otherwise, using a linear probability model. Robust standard errors are in parentheses. * significant

at 10%; ** significant at 5%; *** significant at 1%.

Table 4 shows that males did not drop out more than females when facing increased competition,

supporting the idea that the gender differences found above are not due to omitting students who

failed to complete courses. The double cohort did increase the percentage of courses being dropped,

29Note that courses for which the final grade is below 30 percent are also considered as dropped. Adding thesegrades to the sample analyzed in Table 3 would make the estimates for ‘Male × DC’ slightly larger—the estimatesbeing around 1.2–1.3 points.

23

all else equal: the estimated increase in dropout rates for an ‘average’ student is between 1.2 and 2.4

percentage points.30 This is significant since dropped courses represent about 8 percent of observed

course outcomes in the sample. Overall, results from Table 4 do not suggest that results presented

in Table 3 are due to gender differences in the dropping-out decision process.

7.2 Participation

The experimental economics literature not only suggests that males perform better when faced

with more intense competition than females, but also that females might shy away from it.31 If

a disproportionate number of females avoided the double cohort (e.g. by delaying their university

application), and if these females would have been more adversely affected by the increased com-

petition, then the estimates presented in Table 3 might underestimate the impact of competition

on the performance gap. In order to investigate this possibility, Table 5 presents numbers on the

proportion of female students by status (applied and enrolled), and by year. Both the proportions

of female applicants (Panel A) and the proportions of female among enrolled students (Panel B)

suggest that females did not try to avoid the double cohort more than males. Whether I look at the

female proportions among all students, or by quartiles (based on high school average), I do not see

any economically or statistically significant differences in the proportions of female applicants or

enrolled students. These results are not sensitive to the inclusion or exclusion of G12 students. The

cost of delaying university enrollment by a year might be large compared to the cost of entering

a more competitive environment, which could explain why we do not see changes in the female

proportions of applicants and enrolled students between 2001 and 2003.

Figure 1 suggests that 2002 was not a typical year in terms of university applications, which is

why I use 2001 (not 2002) as a control year in my regression analysis. Nevertheless, the 2002 data

can be used to further investigate whether relatively more females tried to avoid the double cohort.

This is not the case: The female proportion among fast-trackers decreased by (a non-statistically

significant) 1.9 percentage points between 2001 and 2002, and stayed virtually unchanged for the

general student population. Another way female students could have tried to avoid the increased

competition is by enrolling in programs that were ‘less competitive.’ Looking at the proportion of

female students per program across time does not suggest that this is cause for concern. The only

program for which the proportion of female students changed significantly between 2001 and 2003 is

30Although the parameter estimates for ‘Double Cohort’ and ‘HS Average × DC’ are not individually statisticallysignificant when looking at G12 and G13 students, the null hypothesis H0 : π + 88ρ = 0 is rejected at a 10 percentconfidence level under every specification.

31Experimental studies such as Gupta, Poulsen, and Villeval (2013), and Niederle and Vesterlund (2007) find thatmales are more inclined to participate in competitive activities. Flory, Leibbrandt, and List (2010) suggest that thisgender difference also holds in a natural environment. Dohmen and Falk (2011) suggest that risk attitudes play arole in explaining this finding, while Booth and Nolen (2012) and Gneezy, Leonard, and List (2009) suggest that therole of nurture is important in this context. Interestingly, Gneezy et al. (2009) and Andersen et al. (2013) find thatfemales’ and males’ tastes for competition differ whether we are looking at a patriarchal or matrilineal society. Malesare more competitive than females in a patriarchal society, while it is not the case in a matrilineal society. See Crosonand Gneezy (2009) and Niederle and Vesterlund (2011) for more complete (and more general) discussions of genderdifferences in preferences.

24

Table 5: Female Participation by Student Status and Year

Number of Students Female Proportion Difference in ProportionsStudent Status 2001 2003 2001 2003 %2003 - %2001

A. Applied:Bottom Quartile 2,176 4,072 0.571 0.557 -0.014Second Quartile 2,226 4,267 0.576 0.572 -0.004Third Quartile 2,174 4,082 0.591 0.598 0.007Top Quartile 2,250 4,230 0.608 0.611 0.004Total 8,745 16,651 0.586 0.585 -0.001

B. Enrolled:Bottom Quartile 661 929 0.560 0.550 -0.011Second Quartile 627 898 0.596 0.615 0.018Third Quartile 660 978 0.629 0.650 0.022Top Quartile 660 901 0.658 0.644 -0.014Total 2,608 3,706 0.611 0.615 0.004

Note.–The table displays the number of Grade 13 and Grade 12 (combined) students by status (i.e. applied, and en-

rolled) and by year. The quartiles are based on the distributions student high school average. From bottom to top,

these quartiles were for 2001 and for 2003. The last column presents the difference in female student proportion and

results from testing the null hypothesis of equal proportions across years against the alternative hypothesis that they

are different. * significant at 10%; ** significant at 5%; *** significant at 1%.

Computer Science. Unfortunately, a couple of specializations which were associated with Computer

Science in 2001 were associated with Life Science in 2003, making it impossible to know whether

the change in the female proportion was due to the double cohort or the change in program. In any

case, this change should not affect my results. This program is the smallest in terms of enrollment

– 470 students out of the 6,000 observed in this paper are enrolled in Computer Science – and it

has the smallest proportion of female students (around 23 percent).

7.3 Pre-University Competition

Results presented so far assume that a student high school grade is a good indicator of academic

ability. Since students knew (since 1997) that university admissions would be more competitive in

2003 than in previous years, it is possible that they reacted by studying more in high school. The

competition level would therefore increase not only in university, but also prior to that. In this case,

the link between academic ability and high school grades might have changed between 2001 and

2003, representing a potential source a bias for the estimator. Two scenarios must be considered.

First, assume that competition was intense at the high school level, which stimulated males

more than females, as suggested by the experimental economics literature, resulting in males out-

performing females with similar academic ability. Consequently, 2003 male academic ability could

be overestimated by their high school average, which would then translate into underestimating the

impact of increased competition on the gender university-performance gap. This situation should

not be a major concern since I already find a positive effect, and it would only make it larger.

The second scenario would be that females were actually more stimulated by the increased high

25

school competition than males. This seems unlikely given that Table 3 suggests that males increased

their university performance relative to females in the more competitive year. Nevertheless, it is

still be possible in principle that females were more stimulated by competition in both high school

and university. For that to be true and to find a positive coefficient to ‘Male × DC’ – as I do

– females’ high school performance would have to have improved significantly more than their

university performance. The 2003 female high school average would have to severely overestimate

ability. In this case, the 2003 high school average could overestimate females’ ability, which would

result in overestimating the impact of increased competition on the gender university-performance

gap.

I investigate this possibility by re-estimating the regressions presented in Table 3, but using

only students whose ability measurement is not likely to have been affected by the double cohort

(i.e. out-of-province students and students that attended a university prior to the University of

Toronto). The results are very similar to the ones using Ontario secondary school students. In

particular, the coefficient estimates for ‘Male × DC,’ although imprecise, fluctuate between 0.70

(when not controlling for course fixed effects or age) and 3.2 (when controlling for course fixed

effects, but not for age). This finding supports the idea that the estimates presented in Table 3 are

not driven by Ontario female student academic ability being significantly overestimated in 2003.32

8 After the First Year

Results from Table 3 suggest that the increased competition following the Ontario double cohort

had an impact on the gender gap in first year university performance. I now show that the double

cohort actually affected the performance gap during most of these students’ undergraduate years.

Table 6 presents estimates of the competition effect on the gender performance gap for students’

first (Year 1) to fourth year (Year 4) in university. Estimates next to ‘Year 1’ are taken from Table 3.

The estimation strategy is exactly the same as the one used above, except that the dependent

variables are students’ upper year averages. Aside from a small drop for students’ third year, the

effect of increased competition is surprisingly stable across years. The estimated coefficients using

students’ fourth year averages vary between 0.75 and 1.08 when controlling for course fixed effects,

being close to the ones obtained using students’ first year averages especially when controlling for

course fixed effects. Despite being of modest size initially, the competition effect could accumulate

over time, affecting the gender gap in attrition rates, in credit accumulation, and, ultimately, in

on-time graduation rates. I now turn to these.

32As an additional robustness check, I re-estimated the regressions presented in Table 3 on a pooled sample ofOntario and out-of-province students, and students who attended a university prior to the University of Toronto.Using a full set of dummy variables and interaction terms (i.e. using a triple-difference estimation approach), I testwhether the academic ability of Ontario female students is significantly overestimated in 2003 (relative to Ontariomale students). If this is the case, then the coefficient estimate of an interaction term between an Ontario secondaryschool dummy (say ‘ON’) and ‘Male × DC’ would be significantly different from 0. The coefficient estimate of thisinteraction term, although imprecise, is very close to 0 in all specifications. This further suggests that the academicability of Ontario female students is not significantly overestimated in 2003.

26

Table 6: Evolution of the Impact of the Double Cohort on the Gender Performance Gap

G13 Students Only G12 and G13 Students(1) (2) (3) (4) (5) (6)

a) Year 1 1.061*** 1.019*** 1.009*** 1.042*** 1.014*** 1.015***(0.362) (0.348) (0.345) (0.341) (0.342) (0.341)

Number of Students 4,298 4,298 4,298 6,000 6,000 6,000b) Year 2 1.036*** 1.035*** 1.003*** 0.950*** 0.974*** 0.985***

(0.340) (0.313) (0.310) (0.297) (0.267) (0.265)Number of Students 3,908 3,908 3,908 5,466 5,466 5,466

c) Year 3 0.801*** 0.821*** 0.809*** 0.918*** 0.884*** 0.893***(0.309) (0.311) (0.311) (0.287) (0.285) (0.286)

Number of Students 3,409 3,409 3,409 4,847 4,847 4,847d) Year 4 1.774*** 1.055*** 1.077*** 1.260*** 0.753*** 0.785***

(0.303) (0.285) (0.284) (0.268) (0.250) (0.249)Number of Students 3,146 3,146 3,146 4,474 4,474 4,474

Course Fixed Effects No Yes Yes No Yes YesAge Control No No Yes No No Yes

Note.–The table reports 24 coefficient estimates of ‘Male × DC’ for university years 1 through 4. The de-

pendent variable in these sets of regressions is the student’s university average. Each estimate comes from a

separate regression. The estimates next to ‘Year 1’ are from Table 3. Clustered standard errors (at the course

level) are in parentheses. * significant at 10%; ** significant at 5%; *** significant at 1%.

8.1 Attrition

From year-to-year, the sample size of observed students decreases as can be seen in Table 6. Some

students will change program, change university, or simply quit. If males and females differ in their

decision to stay in school (or in the Faculty), the estimates found in Table 6 could misrepresent the

evolution of the competition effect. In particular, if some females were forced to quit school due to

bad performances in their first year, then the results from Table 6 might be underestimating the

effect of competition on the gender performance gap. Table 7 investigates this possibility. Using a

similar estimation strategy as above, I regress (using a linear probability model) a dummy variable

equal to 1 if the student dropped out of the sample after one, two, or three years respectively.

Eighteen estimates of the ‘Male × DC’ parameter are presented in Table 7. Most estimates are

small, and statistically insignificant. Some estimates (e.g., based on G13 students observed after

two years), although not statistically significant, are not small when compared to the attrition

rate. Note that these (larger but imprecise) estimates are all negative suggesting, if anything, that

males might have dropped out of the sample less than females. Overall, these results suggest that

dropouts are not driving the results in Table 6.

8.2 Credit Accumulation

While not strong enough to affect important decisions like dropping out of university, the compe-

tition effect might have been strong enough to slow down students and affect credit accumulation,

and the probability that they graduate on time. In order to better measure the magnitude of

27

Table 7: Impact of the Double Cohort on Attrition Rates

Dependent Variable G13 Students Only G12 and G13 StudentsDropped from Sample (1) (2) (3) (4) (5) (6)

a) After 1 Year -0.015 -0.014 -0.014 -0.007 -0.006 -0.006(0.018) (0.018) (0.018) (0.016) (0.016) (0.016)

Attrition Rate 0.091 0.091 0.091 0.089 0.089 0.089b) After 2 Years -0.021 -0.024 -0.023 -0.007 -0.007 -0.007

(0.025) (0.025) (0.025) (0.021) (0.021) (0.021)Attrition Rate 0.207 0.207 0.207 0.192 0.192 0.192

c) After 3 Years -0.003 -2.89e-4 2.83e-4 0.004 0.009 0.009(0.028) (0.028) (0.028) (0.024) (0.024) (0.024)

Attrition Rate 0.268 0.268 0.268 0.254 0.254 0.254Observations 4,298 4,298 4,298 6,000 6,000 6,000

Program Fixed Effects No Yes Yes No Yes YesAge Control No No Yes No No Yes

Note.–The table presents 18 coefficient estimates for ‘Male × DC’ capturing the effect of compe-

tition on the gender gap in the probability to drop out of the sample (used in Table A1). These

estimates are obtained using a set of dummy dependent variables ‘Dropped from Sample After X

Years’ equal to 1, for a specific student, if I do not observe any grades for this student after X years

(in university). These dummy variables are regressed on the same regressors and under the same six

specifications used in Table A1. The estimation was done using a linear probability model. Robust

standard errors are in parentheses. * significant at 10%; ** significant at 5%; *** significant at 1%.

the long-lasting effect of competition on the gender performance gap, I now look at student credit

accumulation. Table 8 presents coefficient estimates for the effect of competition on the gender

differential in credit accumulation. The number of credits accumulated after X years includes the

number of credits earned during year X, but also the number of credits earned over the previous

years. Therefore, the estimated effects presented in Table 8 should be seen as cumulative effects.

The results in the top panel of Table 8 suggest that, if I look at all students, the effect of the

increased competition on the gender performance gap was not strong enough to significantly affect

the number of earned credits. The estimates for ‘Male × DC’ seem to increase in magnitude as we

look at the effect after three and four years, though the standard errors also become larger. The

results are different if I concentrate at students with high school average 88 percent and below –

students who are more likely to fail or drop a course. The bottom panel of Table 8 clearly suggests

that the double cohort affected the gender differential in credit accumaltion among below-average

students. The estimates for ‘Male × DC’ increase steadily as students progress toward graduation.

By the end of their fourth year, male students will have accumulated between 0.6 and 1.0 credits

(more than a ‘standard’ one-semester course) than similar female classmates as a result of the

increased competition.

28

Table 8: Impact of the Double Cohort on Credit Accumulation

Dependent Variable G13 Students Only G12 and G13 StudentsAccumulated Credits (1) (2) (3) (4) (5) (6)

A. All Students:a) After 1 Year 0.048 0.001 3.47e-4 0.048 -0.003 -0.003

(0.062) (0.054) (0.054) (0.052) (0.045) (0.045)b) After 2 Year 0.273** 0.174 0.171 0.175 0.069 0.069

(0.131) (0.124) (0.124) (0.111) (0.105) (0.105)c) After 3 Years 0.412** 0.304 0.298 0.266 0.139 0.139

(0.207) (0.202) (0.202) (0.173) (0.167) (0.167)d) After 4 Years 0.419 0.265 0.256 0.284 0.102 0.101

(0.296) (0.290) (0.290) (0.249) (0.242) (0.242)Observations 4,298 4,298 4,298 6,000 6,000 6,000

B. Below-Average Students:a) After 1 Year 0.063 0.046 0.046 0.015 -0.009 -0.009

(0.086) (0.082) (0.082) (0.073) (0.069) (0.069)b) After 2 Year 0.485*** 0.444** 0.444** 0.288* 0.230 0.232

(0.179) (0.173) (0.173) (0.152) (0.146) (0.146)c) After 3 Years 0.885*** 0.841*** 0.841*** 0.571** 0.499** 0.506**

(0.276) (0.272) (0.272) (0.232) (0.226) (0.226)d) After 4 Years 1.020*** 0.959*** 0.959*** 0.660** 0.562* 0.574*

(0.373) (0.367) (0.367) (0.312) (0.306) (0.306)Observations 2,687 2,687 2,687 3,506 3,506 3,506

Program Fixed Effects No Yes Yes No Yes YesAge Control No No Yes No No Yes

Note.–The table presents 48 coefficient estimates for ‘Male × DC’ capturing the effect of competition on the

gender gap in the number of credits accumulated after X years (in university). The number of credits accumu-

lated after X years is regressed on the same regressors and under the same six specifications used in Table A1.

The number of credits earned is zero for year X (X=2, 3, or 4) if the student is not observed in year X. Robust

standard errors are in parentheses. * significant at 10%; ** significant at 5%; *** significant at 1%.

8.3 Graduation

One final aspect of the academic performance that I consider is on-time graduation. As the effect

of increased competition seems to be long lasting, it could affect the probability that a student

graduates on time (i.e. during the summer following her fourth year). In Table 9, I present results

from regressing an ‘on-time-graduation’ dummy variable on similar control variables used in the

previous regressions.33 The ‘on-time-graduation’ variable is equal to 1 if the student has graduated

from university by July 1st of her fourth year. Unfortunately, the data do not allow me to observe

2003 students after their fourth year. Estimates of the double cohort effect on the gender difference

in the probability of graduating on time are statistically significant and large. They range from

6.4 to 8.1 percentage points. To put the size of the estimates in perspective, about 40 percent of

students observed in Table 3 graduated on time. Prior to the double cohort, male students were

33The results presented in Table 9 are from linear probability models. The results from estimating probit modelsare very similar.

29

Table 9: Impact of the Double Cohort on On-Time Graduation Rates

G13 Students Only G12 and G13 Students(1) (2) (3) (4) (5) (6)

HS Average 0.023*** 0.026*** 0.026*** 0.023*** 0.025*** 0.025***(0.002) (0.002) (0.002) (0.002) (0.002) (0.002)

Double Cohort -0.506* -0.357 -0.351 -0.563** -0.353 -0.355(0.265) (0.267) (0.267) (0.224) (0.225) (0.225)

Male -0.0874*** -0.0662*** -0.0652*** -0.087*** -0.067*** -0.066***(0.019) (0.020) (0.020) (0.019) (0.020) (0.020)

HS Average × DC 0.005 0.003 0.003 0.005** 0.003 0.003(0.003) (0.003) (0.003) (0.003) (0.003) (0.003)

Male × DC 0.081*** 0.070** 0.070** 0.074*** 0.064** 0.064**(0.030) (0.030) (0.030) (0.025) (0.025) (0.025)

Computer Science -0.238*** -0.241*** -0.275*** -0.277***(0.030) (0.030) (0.027) (0.026)

Humanities -0.088*** -0.089*** -0.129*** -0.128***(0.024) (0.024) (0.021) (0.021)

Life Science -0.147*** -0.148*** -0.164*** -0.165***(0.026) (0.026) (0.022) (0.022)

Age -0.034 -0.031**(0.026) (0.013)

Constant -1.542*** -1.677*** -1.035** -1.542*** -1.602*** -1.009***(0.166) (0.174) (0.527) (0.166) (0.172) (0.300)

Observations 4,298 4,298 4,298 6,000 6,000 6,000R-squared 0.063 0.077 0.078 0.065 0.081 0.082

Note.–The table reports the estimates of regressions of a dummy dependent variable equal to 1 if the student grad-

uated by July 1st of her fourth university year; 0 otherwise. The estimation was done using a linear probability

model. Robust standard errors are in parentheses. * significant at 10%; ** significant at 5%; *** significant at 1%.

less likely to graduate on time than females, the difference being around 7 to 9 percentage points.

This difference completely vanished for double-cohort students.34

The estimates presented here must be interpreted with caution. As the abolition of Grade

13 affected university admission standards in 2003, so it could affect the admission standards for

graduate school in 2007. Hence, while part of the effect estimated here could be due to performance,

it is also possible that these estimates are capturing the effect of strategic behavior. Some students

may have been tempted to delay graduate school applications by a year. As mention earlier,

females may not ‘embrace’ competition as much as males. If graduate-school bound female students

delayed (more than males) their graduation to avoid the double cohort, part of the competition

effect presented above would be due to this behavior. Note that this behavior is not likely to

34 The null hypothesis H0 : δ+β = 0 (i.e. that the sum of the ‘Male’ and ‘Male × DC’ coefficients is equal to zero)is not rejected at conventional confidence levels in any of the six regressions. Note that the effect of the double cohortis not statistically significant based on the ‘Double Cohort’ and ‘HS Average × DC’ coefficient estimates. Once Idrop the ‘HS Average × DC’ variable from the regression, the ‘Double Cohort’ coefficient estimate changes to around−0.1 and becomes statistically significant at 1% percent. The ‘Male × DC’ coefficient estimate remains unchangedat around 0.07. These results are not presented here but are available upon request.

30

explain all of the effect since only a fraction of undergraduate students will apply to graduate

school. In order to have an idea of how much of the estimates found above could be due to

strategic behavior, I estimated similar regressions as those presented in Table 9 excluding students

with high school average above 88 percent to concentrate on students who are less likely to apply

to graduate school. The ‘Male × DC’ coefficient estimates are actually larger for ‘lower-ability’

students, as is the case for earned credits, suggesting that the results presented in Table 9 are

not due to such strategic behavior.35 Interestingly, changes in unconditional on-time graduation

proportions between 2001 and 2003 for females and males show that males’ on-time graduation

rate increased significantly (from 33.6 to 38.1 percent) while females’ decreased slightly (43.8 to

41.4 percent). While comparison of changes in unconditional on-time graduation rates suggest that

males’ performance increased while females’ did not change, comparison of changes in conditional

graduation rates (results from Table 9) suggest that females’ graduation rate was significantly

(negatively) affected by the increased competition while males’ was not. Overall, results from

Table 9 suggest a clear difference in the reaction to increased competition by females and males,

and that results from Table 6 are not due to male students taking more time to graduate.

9 Conclusion

This paper has provided new empirical evidence of gender performance differences in response to

increased competition, focusing on long-term tasks carried out in a regular social environment: the

university classroom. The exogenous increase in competition generated by the abolition of Grade 13

allowed me to assess whether the findings from the experimental economics literature carry over to

tasks that a large fraction of individuals of a given age perform over an extended period and which

they have strong incentives to care about. As such, they help to link the experimental evidence to

competitive gender differences in important life outcomes, including those in the labor market.

My results indicate that gender differences in performance under increased competition do carry

over to an important non-experimental setting: performance while in university. The estimated

effects are modest in size but are precisely estimated, and appear to persist: the increased competi-

tion had an economically significant positive impact on males’ on-time graduation rates, especially

for below-average students. The evidence also supports the view that the results are due to differ-

ential changes in effort by gender, rather than self-selection, as indicated by findings regarding the

decisions to apply to university, enroll if accepted, and drop out of courses/programs. (The mod-

est nature of the differential effects on performance by gender helps explain why the self-selection

effects are muted.)

While the results point to differential effort changes by gender, the nature of the task studied in

this paper also allows for competition to affect performance through a peer channel – an important

feature of workplace environments.36 The double cohort, combined with the limited capacity of

35Detailed results for higher- and lower-ability students are available upon request.36See Epple and Romano (2011) and Sacerdote (2011) for recent literature reviews on peer effects in post-secondary

education.

31

universities to expand rapidly, increased the quality of admitted students, and so of peers. Hence the

estimates presented here are likely to capture the combined (net) effect of two potentially significant

mechanisms by which competition could explain stylized facts about the labor market. If female

students benefit more from higher quality peers, as suggested by recent evidence in Stinebrickner

and Stinebrickner (2006), then my results are more surprising, as they would represent conservative

estimates of the impact of increased competition on the male-female performance differential. Still

finding a significant increased-competition impact suggests that the ‘pure’ competition effect due

to changes in effort could be more important than the peer effect in explaining gender differences

in performance.

The results from this study have several implications. First, they indicate that male and female

performance responds differently to an increase in competition for regular every-day tasks that

are long-lasting and for which the outcomes matter to participants. This underlines the potential

for competition to explain some of the gender inequality found in the labor market. The results

also have implications for the delivery of education (e.g. single-sex versus coed schooling) and for

student achievement assessment. In terms of the former, my results suggest that the optimal level

of competition associated with classroom activities for student learning (or effort) may be different

for females and males and that one should take this finding into account when weighing the pros

and cons of single-sex education. One advantage of single-sex classrooms (or schools) would be to

allow teachers to adjust the competition level according to the gender of the student body.

In terms of the latter, the results suggest that performance assessment measures (e.g. bell-curve

marking) found in many universities may not be gender-neutral: a given performance measure can

favor females (or males), depending on the level of competition inside the classroom. Such a finding

naturally raises the question whether we should expect similar results for high school students who

will not go to college – for potential high-school dropouts in particular. If so, the performance

assessment measures could be made more ‘competitive’ by grouping males (who represent the

majority of high school dropouts) together and using tournament-based evaluations or within-class

ability streaming, without negatively affecting female students.

For future work, it would be interesting to investigate the effects of competition in university

on gender differences in performance once in the labor market – beyond the scope the data I

analyze in this study. Doing so would speak even more directly to the relative importance of

gender competition versus discrimination and occupational self-selection in explaining important

gender differences in the labor market, referred to in the Introduction. It would also be interesting to

explore the strength of gender differences in tasks where absolute, rather than relative, performance

can be measured. This would help clarify whether, on the one hand, the cost of effort rose less for

males relative to females, or on the other hand, it fell by more in more competitive environments.

One could also examine possible gender effects for tasks where the role of peers is more rather than

less important, building on the analysis in Stinebrickner and Stinebrickner (2006).

32

References

Andersen, Steffen, Seda Ertac, Uri Gneezy, John A. List, and Sandra Maximiano. 2013. Gender,

competitiveness and socialization at a young age: Evidence from a matrilineal and a patriarchal

society. Review of Economics and Statistics 95, no. 4:1438-43.

Angrist, Joshua D., Daniel Lang, and Philip Oreopoulos. 2009. Incentives and services for college

achievement: Evidence from a randomized trial. American Economic Journal: Applied Economics

1, no. 1:136-63.

Bertrand, Marianne, and Kevin F. Hallock. 2001. The gender gap in top corporate jobs. Industrial

and Labor Relations Review 55, no. 1: 3-21.

Bertrand, Marianne, Claudia Goldin, and Lawrence F. Katz. 2010. Dynamics of the gender gap for

young professionals in the financial and corporate sectors. American Economic Journal: Applied

Economics 2, no. 3:228-55.

Booth, Alison, and Patrick Nolen. 2012. Choosing to compete: How different are girls and boys?

Journal of Economic Behavior & Organization 81, no. 2:542-55.

Calsamiglia, Caterina, Jorg Franke, and Pedro Rey-Biel. 2013. The incentive effects of affirmative

action in a real-effort tournament. Journal of Public Economics 98:15-31.

Croson, Rachel, and Uri Gneezy. 2009. Gender differences in preferences. Journal of Economic

Literature 47, no. 2:448-74.

Dohmen, Thomas, and Armin Falk. 2011. Performance pay and multidimensional sorting: Pro-

ductivity, preferences, and gender. American Economic Review 101, no. 2:556-90.

Ellison, Glenn, and Ashley Swanson. 2010. The gender gap in secondary school mathematics

at high achievement levels: Evidence from the American Mathematics Competitions. Journal of

Economic Perspectives 24, no. 2:109-28.

Epple, Dennis, and Richard E. Romano. 2011. Peer effects in education: A survey of the theory

and evidence. In Handbook of Social Economics Vol. 1B, ed. Jess Benhabib, Matthew O. Jackson,

and Alberto Bisin. Amsterdam: North-Holland.

Firpo, Sergio, Nicole M. Fortin, and Thomas Lemieux. 2009. Unconditional quantile regressions.

Econometrica 77, no. 3:953-73.

Flory, Jeffrey A., Andreas Leibbrandt, and John A. List. 2010. Do competitive work places deter

female workers? A large-scale natural field experiment on gender differences in job-entry decisions.

Working Paper no. 16546, National Bureau of Economic Research, Cambridge, MA.

Fryer, Roland G., and Steven D. Levitt. 2010. An empirical analysis of the gender gap in mathe-

matics. American Economic Journal: Applied Economics 2, no. 2:210-40.

33

Gneezy, Uri, and Aldo Rustichini. 2004. Gender and competition at a young age. American Eco-

nomic Review 94, no. 2:377-81.

Gneezy, Uri, Kenneth L. Leonard, and John A. List. 2009. Gender differences in competition:

Evidence from a matrilineal and a patriarchal society. Econometrica 77, no. 5:1637-64.

Gneezy, Uri, Muriel Niederle, and Aldo Rustichini. 2003. Performance in competitive environ-

ments: Gender differences. Quarterly Journal of Economics 118, no. 3:1049-74.

Gupta, Nabanita Datta, Anders Poulsen, and Marie Claire Villeval. 2013. Gender matching and

competitiveness: Experimental evidence. Economic Inquiry 51, no. 1:816-35.

Hoffmann, Florian and Philip Oreopoulos. 2009a. A professor like me: The influence of instructor

gender on college achievement. Journal of Human Resources 44, no. 2:479-94.

——. 2009b. Professor qualities and student achievement. The Review of Economics and Statistics

91, no. 1: 83-92.

Jurajda, Stepan and Daniel Munich. 2011. Gender gap in performance under competitive pressure:

Admissions to Czech universities. American Economic Review 101 no. 3:514-18.

King, Alan J.C., Wendy Warren, Will Boyce, Peter Chin, Matthew King, and Jean- Claude Boyer.

2002. Double cohort study: Phase 2 report. Technical Report, Social Program Evaluation Group,

Queen’s University.

King, Alan J.C., Wendy Warren, Will Boyce, Peter Chin, Matthew King, Jean- Claude Boyer, and

Barry O’Connor. 2004. Double cohort study: Phase 3 report. Technical Report, Social Program

Evaluation Group, Queen’s University.

——. 2005. Double cohort study: Phase 4 report. Technical Report, Social Program Evaluation

Group, Queen’s University.

Lavy, Victor. 2013. Gender differences in market competitiveness in a real workplace: Evidence

from performance-based pay tournaments among teachers. Economic Journal 123, no. 569:540-73.

Lindo, Jason M., Nicholas J. Sanders, and Philip Oreopoulos. 2010. Ability, gender, and per-

formance standards: Evidence from academic probation. American Economic Journal: Applied

Economics 2, no. 2:95-117.

Morin, Louis-Philippe. 2013. Estimating the benefit of high school for college-bound students:

Evidence of subject-specific human capital accumulation. Canadian Journal of Economics 46, no.

2:441-68.

Niederle, Muriel, and Lise Vesterlund. 2007. Do women shy away from competition? Do men

compete too much? Quarterly Journal of Economics 122, no. 3:1067-1101.

34

——. 2010. Explaining the gender gap in math test scores: The role of competition. Journal of

Economic Perspectives 24, no. 2:129-44.

——. 2011 Gender and competition. Annual Review of Economics 3, no. 1:601-30.

Ors, Evren, Frederic Palomino, and Eloıc Peyrache. 2013. Performance gender-gap: Does compe-

tition matter? Journal of Labor Economics 31, no. 3:443-99.

Price, Joseph. 2008. Gender differences in the response to competition. Industrial and Labor Rela-

tions Review 61, no 3:320-33.

Sacerdote, Bruce. 2001. Peer effects with random assignment: Results for Dartmouth roommates.

Quarterly Journal of Economics 116 no. 2:681-704.

——. 2011. Peer effects in education: How might they work, how big are they and how much do

we know thus far? In Handbook of the Economics of Education Vol. 3, ed. Erik A. Hanushek,

Stephen Machin, and Ludger Woessmann. Amsterdam: North-Holland.

Stinebrickner, Ralph and Todd R. Stinebrickner. 2006. What can be learned about peer effects

using college roommates? Evidence from new survey data and students from disadvantaged back-

grounds. Journal of Public Economics 90, no. 8-9:1435-54.

Wolfers, Justin. 2006. Diagnosing discrimination: Stock returns and CEO gender. Journal of the

European Economic Association 4, no. 2-3:531-41.

35

Appendix A – Alternative Performance Measures

Table A1: Impact of the Double Cohort on the Gender Performance Gap (First-Year Average)

G13 Students Only G12 and G13 Students(1) (2) (3) (4) (5) (6)

HS Average 1.112*** 1.165*** 1.166*** 1.112*** 1.147*** 1.148***(0.030) (0.031) (0.031) (0.030) (0.031) (0.031)

Double Cohort -11.08** -12.25*** -12.11*** -17.44*** -18.34*** -18.36***(4.446) (4.483) (4.485) (3.709) (3.745) (3.744)

Male 0.703** 0.927*** 0.948*** 0.703** 0.851*** 0.859***(0.317) (0.324) (0.324) (0.317) (0.322) (0.322)

HS Average × DC 0.104** 0.115** 0.113** 0.176*** 0.185*** 0.184***(0.051) (0.051) (0.051) (0.042) (0.043) (0.043)

Male × DC 1.131** 1.058** 1.045** 1.070** 1.027** 1.026**(0.489) (0.490) (0.489) (0.419) (0.419) (0.419)

Computer Science -0.970* -1.023* -0.617 -0.630(0.568) (0.570) (0.503) (0.503)

Humanities 0.709* 0.701* 0.493 0.503(0.369) (0.369) (0.313) (0.313)

Life Science -0.928** -0.948** -0.599* -0.606*(0.410) (0.410) (0.341) (0.341)

Age -0.721* -0.255(0.426) (0.214)

Constant -25.62*** -30.18*** -16.42* -25.62*** -28.66*** -23.83***(2.601) (2.692) (8.558) (2.601) (2.666) (4.838)

Observations 4,298 4,298 4,298 6,000 6,000 6,000R-squared 0.334 0.340 0.340 0.346 0.348 0.348

Note.–The dependent variable in these regressions is the student’s credit-weighted first year university average

(excluding Mathematics credits). Robust standard errors are in parentheses. * significant at 10%; ** signifi-

cant at 5%; *** significant at 1%.

36

Table A2: Impact of the Double Cohort on the Gender Performance Gap (First-Year GPA)

G13 Students Only G12 and G13 Students(1) (2) (3) (4) (5) (6)

HS Average 0.100*** 0.104*** 0.104*** 0.100*** 0.103*** 0.103***(0.003) (0.003) (0.003) (0.003) (0.003) (0.003)

Double Cohort -0.933** -1.052*** -1.040*** -1.369*** -1.456*** -1.457***(0.390) (0.393) (0.393) (0.323) (0.325) (0.325)

Male 0.060** 0.086*** 0.087*** 0.060** 0.080*** 0.080***(0.029) (0.030) (0.030) (0.029) (0.029) (0.029)

HS Average × DC 0.009** 0.010** 0.010** 0.014*** 0.014*** 0.014***(0.004) (0.004) (0.004) (0.004) (0.004) (0.004)

Male × DC 0.101** 0.093** 0.092** 0.091** 0.084** 0.084**(0.045) (0.045) (0.045) (0.038) (0.038) (0.038)

Computer Science -0.105** -0.110** -0.083* -0.083*(0.051) (0.052) (0.045) (0.045)

Humanities 0.083** 0.082** 0.060** 0.061**(0.034) (0.034) (0.029) (0.029)

Life Science -0.072* -0.073** -0.045 -0.046(0.037) (0.037) (0.031) (0.031)

Age -0.062 -0.014(0.039) (0.019)

Constant -6.006*** -6.432*** -5.253*** -6.006*** -6.296*** -6.034***(0.228) (0.237) (0.777) (0.228) (0.234) (0.434)

Observations 4,298 4,298 4,298 6,000 6,000 6,000R-squared 0.323 0.330 0.331 0.334 0.337 0.337

Note.–The dependent variable in these sets of regressions is the student’s first-year university GPA (excluding

Mathematics credits). Robust standard errors are in parentheses. * significant at 10%; ** significant at 5%;

*** significant at 1%.

37

Table A3: Double Cohort and Gender Performance Gap in Smaller Sections

G13 Students Only G12 and G13 Students(1) (2) (3) (4) (5) (6)

HS Average 0.804*** 0.855*** 0.855*** 0.804*** 0.857*** 0.857***(0.046) (0.056) (0.056) (0.046) (0.056) (0.056)

Double Cohort 3.662 8.902* 8.755* 2.860 7.837** 7.922**(5.025) (4.537) (4.516) (4.902) (3.708) (3.721)

Male 1.354** 0.558 0.547 1.354** 0.600 0.592(0.558) (0.448) (0.449) (0.558) (0.452) (0.454)

HS Average × DC -0.0464 -0.113** -0.111** -0.0386 -0.100** -0.0991**(0.055) (0.051) (0.051) (0.057) (0.043) (0.044)

Male × DC -0.0476 0.261 0.271 -0.166 0.167 0.168(0.620) (0.509) (0.510) (0.519) (0.385) (0.385)

Age 0.643** 0.454(0.316) (0.297)

Course Fixed Effects No Yes Yes No Yes YesObservations 2,343 2,343 2,343 3,180 3,180 3,180Students 1,964 1,964 1,964 2,691 2,691 2,691R-squared 0.17 0.19 0.19 0.17 0.18 0.18

Note.–The dependent variable in these sets of regressions is a first-year university course grade. A course

section is labeled as ‘small’ if it contains less than thirty students. Clustered standard errors (at the course

level) are in parentheses. * significant at 10%; ** significant at 5%; *** significant at 1%.

38

Appendix B – Competition and Effort

Here, I develop some details regarding the model presented in Section 3.2. Using equation (4),

we can see that as the level of competition increases, effort will increase or decrease depending on

whether students enjoy or dislike competition and on how the university changes the link between

knowledge and grades:

de∗gdl

= −dλldl

∂K(e∗g ,a)

∂e − ∂2Cg(e∗g ,a,l)

∂e∂l

λl∂2K(e∗g ,a)

∂e2− ∂2Cg(e∗g ,a,l)

∂e2

. (6)

The gender difference in the change in effort following an increase in the level of competition is

given by:

∆de∗

dl

∣∣∣∣l=0

=

∂2Cm(e∗m,a,0)∂e∂l − dλl

dl∂K(e∗m,a)

∂e

∣∣∣∣l=0

λ0∂2K(e∗m,a)

∂e2

∣∣∣∣l=0

− ∂2Cm(e∗m,a,0)∂e2

−

∂2Cf (e∗f ,a,0)

∂e∂l − dλldl

∂K(e∗f ,a)

∂e

∣∣∣∣l=0

λ0∂2K(e∗f ,a)

∂e2

∣∣∣∣l=0

− ∂2Cf (e∗f ,a,0)

∂e2

(7)

In the absence of competition (at l = 0), females and males are assumed to have the same knowledge

production and cost functions, and therefore exert the same level of effort, for a given level of ability

(a). Hence, we can simplify equation (7):

∆de∗

dl

∣∣∣∣l=0

= −∂2Cf (e

∗,a,0)∂e∂l − ∂2Cm(e∗,a,0)

∂e∂l

λ0∂2K(e∗,a)

∂e2

∣∣∣∣l=0

− ∂2C(e∗,a,0)∂e2

∣∣∣∣l=0

. (8)

The concavity of the knowledge production function and the convexity of the cost function guarantee

that the denominator of equation (8) is strictly negative. Therefore, the sign of equation (8) will be

determined by whether males enjoy competition more than females. If males enjoy competition more

(i.e. if∂C2

f (e,a,l)

∂e∂l > ∂C2m(e,a,l)∂e∂l ), we would expect to see their effort level and academic performance

increase relative to females as competition increases.

Appendix B.1 – Competition and Effort Incentives (λt)

In this section, I illustrate the potential impact of increased competition and bell-curve marking

on effort incentives. I abstract from potential gender differences in response to competition to

concentrate on the effect of competition on the effort incentives set by a university that grades on

a bell curve.

Imagine a student with ability a will exert effort e to acquire some knowledge, K(e, a). Assume

that K(e, a) is continuously differentiable, increasing and concave in a and e, and that the marginal

benefit of effort increases with ability (i.e. ∂2K(e,a)∂e∂a > 0). The cost of studying is given by a

continuously differentiable function C(e, a) (in e and a), and increasing and convex in e. Further,

assume that the marginal cost of effort is decreasing with ability (i.e. ∂2C(e,a)∂e∂a < 0).

39

Students expect the university to mark on a bell curve. More specifically, they expect that,

every year, the average grade in university will be:

µ = ηt + λtE(K(e, a)|t) (9)

where E(K(e, a)|t) is the average knowledge of students enrolled in year t. The variance of university

grades is also expected to remain constant across time:

σ2 = λ2t var(K(e, a)|t) (10)

Students take the mean and the variance of knowledge (E(K(e, a)|t) and var(K(e, a)|t)) as given

(i.e. they do not think they can individually affect the average performance or its variance). We

can re-write equation (10) to see what will affect λt:

λ2t =σ2

var(K(e, a)|t)

Therefore, is λt is expected to increase as var(K(e, a)|t) decreases. In order to see what hap-

pens to var(K(e, a)|t) (and λt) as competition increases, we must go back to the student utility

maximization problem.

Student utility is simply defined by the difference between her university grade and the effort

she exerted. So her utility maximization problem is:

maxe

ηt + λtK(e, a)− C(e, a)

The first-order condition for this problem is

λt∂K(e∗, a)

∂e− ∂C(e∗, a)

∂e= 0 (11)

We can see that student effort will increase as λt increases. Importantly, we can use equation (11)

to show that

de∗

da=λt

∂2K(e∗,a)∂e∂a − ∂2C(e∗,a)

∂e∂a∂2C(e∗,a)

∂e2− λt ∂

2K(e∗,a)∂e2

> 0 (12)

That is, higher ability students will exert more effort. Since de∗

da is strictly positive and that C(e, a)

and K(e, a) are continuously differentiable, there is a one-to-one correspondence between a and e.

We can therefore define

H(a) ≡ K(e∗(a), a)

Now we can look at what happens when competition for university admissions increases from

one year to the other. It is easy to imagine that if high school grades are determined in a similar

40

fashion to university grades, the ability threshold that determines whether a student is accepted

in university will go up during the more competitive year. Therefore, as competition for admission

increases, the variance of university-student ability should decrease while their average ability will

increase as universities become more selective – the ability distribution is being truncated from

below.

We can see what will happen to the variance of H(a) if the variance of a decreases using a

Taylor approximation:

var[H(a)|t] ≈ [H ′(E(a)|t)]2 + var(a|t) (13)

Under mild conditions H(a) is concave.37 If H(a) is concave then as competition increases,

H ′(E(a)|t) will decrease and so will var[H(a)|t]. This means that the variance of knowledge

var(K(e, a)|t) will be smaller and λt larger (due to equation (10)) in a competitive year and con-

sequently, the optimal level of effort for a given a, e∗(a), will be higher in a competitive year (due

to equation (11)). This discussion indicates that although effort is not observable here, one could

imagine that the increased benefit to effort is one important channel through which competition

affects students’ performance.

Appendix B.2 – Concavity of H(a)

We know that H(a) is increasing in a:

∂H(a)

∂a=

∂K(e(a), a)

∂a+∂K(e(a), a)

∂e(a)

de(a)

da> 0

The second derivative of H(a) is given by:

∂2H(a)

∂a2=

∂2K(e(a), a)

∂a2+ 2

∂2K(e(a), a)

∂a∂e(a)

de(a)

da

+∂2K(e(a), a)

∂e(a)2

(de(a)

da

)2

+∂K(e(a), a)

∂e(a)

d2e(a)

da2(14)

The first and third terms of equation (14) are negative while the second term is positive. In order

for the sum of these three terms to be negative, the ‘complementarity’ between ability and effort

must not be too large in the production of knowledge. That is, the concavity of the knowledge

production function must dominate the ‘complementarity’ effect. A similar condition is sufficient

for d2e(a)da2

to be negative. To simplify the exposition, I rewrite the first-order condition as

∂R(e∗(a), a)

∂e= λt

∂K(e∗, a)

∂e− ∂C(e∗, a)

∂e(15)

37Loosely speaking, H(a) will be concave if the concavity of the knowledge production function in effort and abilitydominates the ‘complementarity’ of these two inputs. The exact conditions for the concavity of H(a) are presentedin Appendix B.2.

41

Now, from equation (12), we have:

de∗

da= −

∂2R(e(a),a)∂e∂a

∂2R(e(a),a)∂e2

(16)

So,

d2e∗

da2=−(∂2R(e(a),a)

∂e2

)(∂3R(e(a),a)∂e∂a2

+ ∂3R(e(a),a)∂e2∂a

de∗

da

)+(∂2R(e(a),a)

∂e∂a

)(∂3R(e(a),a)∂e2∂a

+ ∂3R(e(a),a)∂e3

de∗

da

)(∂2R(e(a),a)

∂e2

)2≡ A

B

Since B is always positive, the sign of d2e∗

da2will be determined by the sign of A. Using equation

(16), we can re-write A as:

A = −∂2R(e(a), a)

∂e2∂3R(e(a), a)

∂e∂a2+ 2

∂3R(e(a), a)

∂e2∂a

∂2R(e(a), a)

∂e∂a

−(∂2R(e(a), a)

∂e∂a

)2(∂3R(e(a),a)

∂e3

∂2R(e(a),a)∂e2

)

In order to guarantee A to be negative, the ‘complementarity’ between a and e in creating knowledge

must decrease with effort and ability, and the third derivative of R with respect to effort must be

negative. That is, a sufficient (but not necessary) condition is:

∂3R(e(a), a)

∂e3< 0

∂3R(e(a), a)

∂e∂a2< 0

∂3R(e(a), a)

∂e2∂a< 0.

42